The Add Media page changed at the end of the last year and I think it is better now. It has all of the functions the old one had, but I don' t have an idea about your problem of inserting a picture from URL.

The code view can be reached from the Text button on the right side of the text editing options, on the editing page of any post.

Since you mention the "Fetch Photo button", you're talking about the New Post tool in the grey admin bar. This is meant for quick posting - it doesn't support all the options that are normally available. More important, it's buggy: your content may disappear, partly or completely. Users have been complaining about this for almost a year, and so far WP has found nothing to say (or do) about it.
So, simply don't use that tool: create your posts via Posts > Add New in your dashboard sidebar.